First off, good job for taking some time to think this out correctly. It is never good to make a rash or impulsive decision when the result could have a big impact on your life down the road.
As far as the quantity vs. quality question, I'd say do your best to focus on both. It is always good to identify your long term goal, and make informed decisions along the way that will make you the most marketable and qualified for that specific goal. It appears as though you have already identified the airlines as a target track, so that is a good starting point. My suggestion would be to somehow obtain your CFI/I/MEI, start instructing, and take advantage of the 135/91 opportunity. This will allow you to start building important PIC time, as well as get exposure to a wide variety of situations while flying the more complex aircraft in the “real world” IFR system and actual weather.
Let me expand on each. You are correct, that working as a CFI for a while is a widely accepted and respected way of building time. As many have said before, as well as myself, you really start to truly learn when you teach. It is an excellent way to become very strong in the knowledge areas, and somewhat proficient on the hands-on aspect of flying, depending on how much you demo things to your students (which you will see is beneficial for both of you for different reasons). As I mentioned before, a very important thing is that you are building PIC time on every flight, which will begin to look very good on paper. You will become very good at decision making, and any employer, be it airline, corporate, cargo, or whatever will love to see it. It is interesting that in the progression of a pilot’s career, being a PIC will teach you how to become a good SIC, and then being that SIC will teach you new things on how to become a PIC again.
The 135/91 opportunity produces that “quality” time that you are looking for, and definitely should be pursued. This is great because it will help you compensate for the areas in which instructing lacks. You will find that after instructing for a while, you fall victim to the “bubble effect”. By this I mean that you are using the same runways, the same frequencies, talking to the same controllers, flying the same maneuvers, over the same roads and fields, in mostly the same weather conditions, all the time. Once you break out of that bubble, and see the “real world”, it all starts to click. It will make you an even better instructor, because it will allow you to come back to your students, and teach them the same maneuvers and concepts as before, but with a new and fresh outlook based on what you see and learn yourself in the “real world”. Another advantage is the opportunity to fly alongside an experienced pilot, and get some exposure to a crew cockpit environment. Every single airline interview will most likely include some questions on your thoughts or experience with CRM. Flying 135 up in the soup, taking on ice in the winter, dodging storms in the summer, and the occasional system abnormality will undoubtedly give you some good practice at inter-cockpit communication and will give you some material to use to impress your interview panel.
The disclaimer here is to make sure that any SIC time you do log is legit. It can be quite a grey area, so do your homework and read up on the regs. Take into account the particulars of the aircraft, as well as the operating specs of the 135 outfit. You would never want to show up to interview, and have them catch illegitimate flight time in your logbook.
Hope this helps...good luck.